S-shaped stress profiles and methods of making

ABSTRACT

A strengthened glass having a stress profile that differs from error-function and parabolic profiles. Stress relaxation and thermal annealing/diffusion effects, which occur at longer ion exchange and/or anneal times increase the depth of compression of the surface layer. A method of achieving these effects is also provided.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.16/837,286, filed Apr. 1, 2020, which is a continuation of U.S.application Ser. No. 15/372,520, filed Dec. 8, 2016, which claims thebenefit of priority under 35 U.S.C. § 119 of U.S. ProvisionalApplication Ser. No. 62/280,376, filed Jan. 19, 2016, and U.S.Provisional Application Ser. No. 62/264,495, filed Dec. 8, 2015, thecontents of which are relied upon and incorporated herein by referencein their entirety.

BACKGROUND

The disclosure relates to strengthened glass. More particularly, thedisclosure relates to strengthened glass having a deep compressivelayer.

Glasses strengthened by ion exchange tend to exhibit stress profilesthat resemble a complementary error function or a parabolic function.While such stress profiles provide adequate protection for certain typesof damage, such as sharp impacts, they do not provide sufficientprotection for other types of insult, such as a drop from a height ontoan abrasive surface.

SUMMARY

The present disclosure provides a strengthened glass having a stressprofile that differs from error-function and parabolic profiles thathave previously been observed for such glasses. Stress relaxation andthermal annealing/diffusion effects, which occur at longer ion exchangeand/or anneal times, increase the depth of compression (DOC) of thesurface layer. A method of achieving these effects is also provided.

Accordingly, one aspect of the disclosure provides a glass articlehaving a thickness (t) and a center at t/2. The glass has a firstcompressive layer under a first compressive stress (CS1), thecompressive layer extending from a first surface of the glass to a firstdepth of compression (DOC1). The stress in the glass varies as afunction of the thickness (t) to form a stress profile comprising: afirst region extending from the first surface to a depth (d1) into theglass, wherein d1>0.06t and wherein at least a portion of the firstregion has a first slope (m1); and a second region extending from adepth of at least d1 to the first depth of compression (DOC1) and havinga second slope (m2), wherein |m1|≤|m2|.

Another aspect of the disclosure provides a glass article strengthenedby ion exchange, the glass article having a thickness (t) and a centerat t/2. The glass article comprises: a compressive region on either sideof the center, wherein the compressive region extends from a surface ofthe glass article to a depth of compression (DOC) and is under acompressive stress; and a tensile region extending from the depth ofcompression (DOC) to the center of the glass article, wherein thetensile region is under a physical center tension (CT). The stress inthe glass varies as a function of the thickness (t) to form a stressprofile comprising a sub-region within the compressive region in whichthe stress profile has a negative curvature, wherein the maximumabsolute value of the negative curvature is between 20 MPa/(t(mm))² and4,000 MPa/(t(mm))².

Yet another aspect of the disclosure provides a glass articlestrengthened by an ion exchange process followed by a thermaldiffusion/annealing step. The glass article has a thickness (t) and acenter at t/2, and a first compressive layer under a first compressivestress (CS1) that extends from a first surface of the glass to a firstdepth of compression (DOC1). The glass also comprises a tensile regionextending from the first depth of compression (DOC1) to the center ofthe glass that is under a physical center tension (CT). The stress inthe glass varies as a function of the thickness (t) to form a stressprofile. The stress profile comprises: a first region extending from thefirst surface to a depth (d1) into the glass, wherein d1>0.06t andwherein at least a portion of the first region has a first slope (m1);and a second region extending from a depth of at least d1 to the firstdepth of compression (DOC1) and having a second slope (m2), wherein|m1|≤|m2|.

Still another aspect of the disclosure provides a method ofstrengthening a glass comprising first alkali cations. The glass has afirst surface, a second surface opposite the first surface, a thickness(t), and a center at t/2. The method comprises: immersing the glass inan ion exchange bath comprising second alkali cations, wherein thesecond alkali cations are different from the first alkali cations, andreplacing the first alkali cations within the glass with the secondalkali cations from the ion exchange bath to form a compressive layerextending from the first surface and second surface of the glass to afirst depth of compression (DOC1), where the compressive layer is undera first compressive stress (CS1) at the surface; and diffusing thesecond alkali cations from the first surface and the second surface tothe center of the glass. The stress in the glass varies as a function ofthe thickness (t) to form a stress profile. The stress profilecomprises: a first compressive region extending from each of the firstsurface and the second surface to a depth (d1) into the glass, whereind1>0.06t and wherein at least a portion of the first region has a firstslope (m1), and a second compressive stress (CS2) at each of the firstsurface and the second surface, wherein CS2≤CS1; and a secondcompressive region extending from a depth of at least d1 to a seconddepth of compression (DOC2) and having a second slope (m2), wherein|m1|≤|m2|, and wherein DOC2>DOC1.

In a first aspect a glass article is provided. The glass articlecomprises: a thickness t, a center located at t/2, a first compressivelayer extending from a first surface of the glass article to a firstdepth of compression DOC1, and a first maximum compressive stress CS1within the first compressive layer. The first compressive layer has astress profile. The stress profile comprises a first region extendingfrom the first surface to a depth d1 into the glass article, whereind1>0.06t, and at least a portion of the first region has a first slopem1, and a second region extending from a depth of at least d1 to thefirst depth of compression DOC1 and having a second slope m2, wherein|m1|≤|m2|.

In a second aspect, the glass article of the first aspect is providedwherein the stress profile comprises a sub-region within the compressiveregion with a negative curvature, wherein the maximum absolute value ofthe negative curvature is at d1.

In a third aspect, the glass article of any of the preceding aspects isprovided wherein the maximum absolute value of the negative curvature isbetween 20 MPa/(t(mm))2 and 4,000 MPa/(t(mm))2.

In a fourth aspect, the glass article of any of the preceding aspects isprovided wherein a slope of the stress profile at d1 is zero.

In a fifth aspect, the glass article of any of the preceding aspects isprovided wherein DOC1≥0.2t.

In a sixth aspect, the glass article of any of the preceding aspects isprovided wherein CS1>0, m1>0 and m2<0.

In a seventh aspect, the glass article of any of the preceding aspectsis provided wherein t is in a range from about 0.1 mm to about 2 mm.

In an eighth aspect, the glass article of any of the preceding aspectsis provided wherein DOC1 is in a range from about 0.14t to about 0.35t.

In a ninth aspect, the glass article of any of the preceding aspects isprovided wherein; the first maximum compressive stress CS1 is at thefirst surface and is in a range from about 500 MPa to about 2,000 MPa,and the stress profile further comprises a second sub-region having apositive curvature.

In a tenth aspect, the glass article of any of the preceding aspects isprovided wherein the negative curvature of the first sub-region has anabsolute value exceeding 10 MPa/(t(mm))² over a spatial extent rangingfrom about 2% to about 25% of t.

In an eleventh aspect, the glass article of any of the preceding aspectsis provided wherein: the first maximum compressive stress CS1 is at thefirst surface, and the compressive stress decreases to less than 50% ofthe first maximum compressive stress CS1 at a depth of less than about 8μm below the first surface.

In a twelfth aspect, the glass article of any of the preceding aspectsis provided further comprising a physical center tension in a range fromabout 40 MPa/(t(mm))1/2 to about 150 MPa/(t(mm))1/2.

In a thirteenth aspect, the glass article of any of the precedingaspects is provided wherein the second region of the stress profilecomprises an inflection point.

In a fourteenth aspect, the glass article of any of the precedingaspects is provided wherein: the first region of the stress profilefurther comprises a sub-region extending from the first surface to adepth d2, d2<d1, the sub-region comprising at least a portion with athird slope m3, |m1|<|m3|, and 30 MPa/μm≤|m3|≤200 MPa/μm.

In a fifteenth aspect, the glass article of any of the preceding aspectsis provided wherein 50 MPa/μm≤|m3|≤200 MPa/μm.

In a sixteenth aspect, the glass article of any of the preceding aspectsis provided wherein the glass article comprises an alkalialuminosilicate glass.

In a seventeenth aspect, the glass article of the sixteenth aspect isprovided wherein the alkali aluminosilicate glass comprises at leastabout 4 mol % P₂O₅, wherein (M₂O₃(mol %)/R_(x)O(mol %))<1, whereM₂O₃=Al₂O₃+B₂O₃, and where R_(x)O is the sum of monovalent and divalentcation oxides present in the alkali aluminosilicate glass.

In an eighteenth aspect, the glass article of the sixteenth aspect isprovided wherein the alkali aluminosilicate glass comprises:

-   -   about 40 mol % to about 70 mol % SiO₂;    -   about 11 mol % to about 25 mol % Al₂O₃;    -   about 2 mol % to about 15 mol % P₂O₅;    -   about 10 mol % to about 25 mol % Na₂O;    -   about 10 to about 30 mol % R_(x)O, where R_(x)O is the sum of        the alkali metal oxides, alkaline earth metal oxides, and        transition metal monoxides present in the glass.

In a ninetieth aspect, the glass article of any of the preceding aspectsis provided further comprising: a second compressive layer extendingfrom a second surface of the glass article opposite the first surface toa second depth of compression DOC2, a second maximum compressive stressCS2 within the second compressive layer, and a tensile region extendingfrom DOC1 to DOC2.

In a twentieth aspect, the glass article of the nineteenth aspect isprovided wherein DOC1=DOC2.

In a twenty-first aspect a glass article is provided. The glass articlecomprises: a thickness t, a center located at t/2, a compressive regionlocated between a surface of the glass article and the center, whereinthe compressive region is under a compressive stress and extends fromthe surface to a depth of compression DOC; a sub-region within thecompressive region in which a stress profile has a negative curvature,wherein the maximum absolute value of the negative curvature is between20 MPa/(t(mm))2 and 4000 MPa/(t(mm))2; and a tensile region extendingfrom the depth of compression DOC to at least the center of the glassarticle, wherein the tensile region is under a physical center tensionCT.

In a twenty-second aspect, the glass article of the twenty-first aspectis provided wherein t is in a range from about 0.1 mm to about 2 mm.

In a twenty-third aspect, the glass article of the twenty-first ortwenty-second aspect is provided wherein DOC is in a range from about0.14t to about 0.35t.

In a twenty-fourth aspect, the glass article of any of the twenty-firstthrough twenty-third aspects is provided wherein: a maximum compressivestress CS1 is at the first surface and is in a range from about 500 MPato about 2,000 MPa, and the compressive region further comprises asub-region in which the stress profile has a sub-region of positivecurvature.

In a twenty-fifth aspect, the glass article of any of the twenty-firstthrough twenty-fourth aspects is provided wherein: the glass article hasa maximum compressive stress CS1 at the surface, and the compressivestress decreases to less than 50% of the maximum compressive stress at adepth of less than about 8 μm below the surface.

In a twenty-sixth aspect, the glass article of any of the twenty-firstthrough twenty-fifth aspects is provided wherein the negative curvaturehas an absolute value exceeding 10 MPa/t² over a sub-region, thesub-region having a spatial extent ranging from about 2% to about 25% oft.

In a twenty-seventh aspect, the glass article of any of the twenty-firstthrough twenty-sixth aspects is provided wherein CT is in a range fromabout 40 MPa/(t(mm))^(1/2) to about 150 MPa/(t(mm))^(1/2).

In a twenty-eighth aspect, the glass article of any of the twenty-firstthrough twenty-seventh aspects is provided wherein the glass articlecomprises an alkali aluminosilicate glass.

In a twenty-ninth aspect, the glass article of the twenty-eighth aspectis provided wherein the alkali aluminosilicate glass comprises at leastabout 4 mol % P₂O₅, wherein (M₂O₃(mol %)/R_(x)O(mol %))<1, whereinM₂O₃=Al₂O₃+B₂O₃, and wherein R_(x)O is the sum of monovalent anddivalent cation oxides present in the alkali aluminosilicate glass.

In a thirtieth aspect, the glass article of the twenty-eighth aspect isprovided wherein the alkali aluminosilicate glass comprises: about 40mol % to about 70 mol % SiO₂; about 11 mol % to about 25 mol % Al₂O₃;about 2 mol % to about 15 mol % P₂O₅; about 10 mol % to about 25 mol %Na₂O; about 13 to about 30 mol % R_(x)O, where R_(x)O is the sum of thealkali metal oxides, alkaline earth metal oxides, and transition metalmonoxides present in the glass.

In a thirty-first aspect a method of strengthening a glass is provided.The method comprising: immersing a glass comprising first alkali cationsin an ion exchange bath comprising second alkali cations to replace thefirst alkali cations within the glass with the second alkali cationsfrom the ion exchange bath and form a first compressive layer extendingfrom a first surface of the glass, wherein the glass has a thickness t,the second alkali cations are different from the first alkali cations,the first surface is opposite a second surface, the first compressivelayer extends from the first surface to a first depth of compressionDOC1, and the first compressive layer has a first compressive stressCS1; and diffusing the second alkali cations from the first surface to acenter of the glass located at t/2, wherein stress in the glass variesas a function of the depth in the glass to form a stress profile. Thestress profile comprises a first compressive region extending from thefirst surface to a depth d1 in the glass, wherein d1>0.06t, and at leasta portion of the first region has a first slope m1, and a secondcompressive stress CS2 at the first surface, wherein CS2≤CS1; and asecond compressive region extending from a depth of at least d1 to asecond depth of compression DOC2 and having a second slope m2, wherein|m1|≤|m2|, and DOC2>DOC1.

In a thirty-second aspect, the method of the thirty-first aspect isprovided wherein immersing the glass in the ion exchange bath comprisingthe second alkali cations also replaces the first alkali cations withinthe glass with the second alkali cations from the ion exchange bath toform a second compressive layer extending from the second surface of theglass.

In a thirty-third aspect, the method of the thirty-second aspect isprovided wherein the first compressive layer and the second compressivelayer are formed simultaneously.

In a thirty-fourth aspect, the method of any of the thirty-first throughthirty-third aspects is provided wherein a slope of the stress profileat d1 is zero.

In a thirty-fifth aspect, the method of any of the thirty-first throughthirty-fourth aspects is provided wherein the diffusing comprises athermal diffusion step comprising heating the glass to a temperature ina range from about 400° C. to about 500° C.

In a thirty-sixth aspect, the method of the thirty-fifth aspect isprovided wherein the thermal diffusion step comprises heating the glassfor at least about 16 hours at the temperature.

In a thirty-seventh aspect, the method of any of the thirty-firstthrough thirty-sixth aspects is provided wherein the ion exchange bathcomprises at least 30 wt % of a salt comprising the first alkalications.

In a thirty-eighth aspect, the method of any of the thirty-first throughthirty-seventh aspects is provided further comprising immersing theglass in a second ion exchange bath following the step of immersing theglass in the ion exchange bath to form a surface compressive regioncomprising a third compressive stress CS3 at the first surface, whereinCS3>CS1.

In a thirty-ninth aspect, the method of the thirty-eighth aspect isprovided wherein the second ion exchange bath comprises at least about90 wt % of a salt comprising the second alkali cations.

In a fortieth aspect, the method of any of the thirty-first throughthirty-ninth aspects is provided wherein the glass comprises an alkalialuminosilicate glass.

In a forty-first aspect, the method of the fortieth aspect is providedwherein the alkali aluminosilicate glass comprises at least about 4 mol% P₂O₅, wherein (M₂O₃(mol %)/R_(x)O(mol %))<1, M₂O₃=Al₂O₃+B₂O₃, andR_(x)O is the sum of monovalent and divalent cation oxides present inthe alkali aluminosilicate glass.

In a forty-second aspect, the method of the fortieth aspect is providedwherein the alkali aluminosilicate glass comprises: about 40 mol % toabout 70 mol % SiO₂; about 11 mol % to about 25 mol % Al₂O₃; about 2 mol% to about 15 mol % P₂O₅; about 10 mol % to about 25 mol % Na₂O; about10 to about 30 mol % R_(x)O, where R_(x)O is the sum of the alkali metaloxides, alkaline earth metal oxides, and transition metal monoxidespresent in the glass.

In a forty-third aspect, the method of any of the thirty-first throughforty-second aspects is provided wherein the stress profile comprises asub-region within the compressive region with a negative curvature,wherein the maximum absolute value of the negative curvature is at d1.

In a forty-fourth aspect, the method of forty-third aspect is providedwherein the maximum absolute value of the negative curvature is between20 MPa/(t(mm))² and 4,000 MPa/(t(mm))².

In a forty-fifth aspect a consumer electronic product is provided. Theconsumer electronic product comprising: a housing having a frontsurface, a back surface and side surfaces; electrical componentsprovided at least partially within the housing, the electricalcomponents including at least a controller, a memory, and a display, thedisplay being provided at or adjacent the front surface of the housing;and the glass article of any of the first through thirtieth aspectsdisposed over the display.

These and other aspects, advantages, and salient features will becomeapparent from the following detailed description, the accompanyingdrawings, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-sectional view of a strengthened glassarticle.

FIG. 2 is a plot of modeled and measured stress profiles of ionexchanged glasses having a thickness of 800 μm as a function ofdiffusion time.

FIG. 3 is a detailed view of the stress profile in FIG. 2 .

FIG. 4 is a plot of modeled and measured stress profiles for glasses ionexchanged for 40 hours at 460° C.

FIG. 5 is a plot of modeled and measured stress profiles for glass thatwas ion exchanged at 460° C. for 60 hours and then ion exchanged at 490°C. for 32 hours.

FIG. 6 is a plot of stress profiles measured for glass ion exchanged at460° C. for 28 hours in mixed KNO₃/NaNO₃ baths of differentcompositions.

FIG. 7 is a plot of the modeled stress profile and measured stressprofile obtained for glass ion exchanged at 460° C. for 28 hours in abath containing 41 wt % NaNO₃.

FIG. 8 is a plot of modeled and measured stress profiles of a 0.5 mmthick glass ion exchanged for 7 hours at 410° C. in a bath of 100 wt %KNO₃, and then thermally diffused by heating for 5 hours at 450° C.

FIG. 9 is a plot of modeled and measured stress profiles of a 0.5 mmthick glass ion exchanged for 24 hours at 460° C. in a bath of pure (100wt %) KNO₃ and then thermally diffused by heating at 450° C. for timesranging from 5 hours to 24 hours.

FIG. 10 is a plot of modeled and measured stress profiles of a 0.8 mmthick glass ion exchanged for 24 hours at 460° C. in a bath of pure (100wt %) KNO₃ and then thermally diffused by heating at 450° C. for timesranging from 5 hours to 24 hours.

FIG. 11 is a plot of an S-shaped profile obtained for 0.4 mm thick glassion exchanged for 11.5 hours at 430° C. in a bath containing 17 wt %NaNO₃ and 83 wt % KNO₃, and then thermally treated at 430° C. for 13.07hours.

FIG. 12 is a schematic representation of stress profiles of a glassarticle following a first ion exchange and subsequent thermal treatment.

FIG. 13 is a schematic representation of stress profiles of a glassarticle following a first ion exchange, thermal treatment, and a secondion exchange.

FIG. 14 is a plot of stress profiles of glasses obtained following afirst ion exchange, thermal treatment, and a second ion exchange.

FIG. 15 is a plot of the index profile for transverse magnetic andtransverse electric guided light obtained for 0.4 mm glass ion exchangedfor 11 hours at 450° C. in a bath containing 38 wt % NaNO₃ and 62 wt %KNO₃, heat treated for 6.5 hours at 420° C., and then ion exchanged for11 minutes at 390° C. in a bath containing 0.5 wt % NaNO₃ and 99.5 wt %KNO₃.

FIG. 16 is a plot of a stress profile extracted from the index profilesof FIG. 15 .

FIG. 17 is a plan view of an exemplary electronic device incorporatingany of the strengthened articles disclosed herein.

FIG. 18 is a perspective view of the exemplary electronic device of FIG.17 .

DETAILED DESCRIPTION

In the following description, like reference characters designate likeor corresponding parts throughout the several views shown in thefigures. It is also understood that, unless otherwise specified, termssuch as “top,” “bottom,” “outward,” “inward,” and the like are words ofconvenience and are not to be construed as limiting terms. In addition,whenever a group is described as comprising at least one of a group ofelements and combinations thereof, it is understood that the group maycomprise, consist essentially of, or consist of any number of thoseelements recited, either individually or in combination with each other.Similarly, whenever a group is described as consisting of at least oneof a group of elements or combinations thereof, it is understood thatthe group may consist of any number of those elements recited, eitherindividually or in combination with each other. Unless otherwisespecified, a range of values, when recited, includes both the upper andlower limits of the range as well as any ranges therebetween. As usedherein, the indefinite articles “a,” “an,” and the correspondingdefinite article “the” mean “at least one” or “one or more,” unlessotherwise specified. It also is understood that the various featuresdisclosed in the specification and the drawings can be used in any andall combinations.

As used herein, the terms “glass article” and “glass articles” are usedin their broadest sense to include any object made wholly or partly ofglass. Unless otherwise specified, all compositions are expressed interms of mole percent (mol %).

As described herein, compressive stress (CS) and central tension orphysical center tension (CT) are expressed in terms of megaPascals(MPa), depth of layer (DOL) and depth of compression (DOC) may be usedinterchangeably and are expressed in terms of microns (μm), where 1μm=0.001 mm, and, unless otherwise specified, thickness (t) is expressedherein in terms of millimeters, where 1 mm=1,000 μm. Compressive stress(CS) is expressed herein as a positive value and central tension andphysical center tension (CT) are expressed as negative values.

Compressive stress (including surface CS) is measured by surface stressmeter (FSM) using commercially available instruments such as theFSM-6000, manufactured by Orihara Industrial Co., Ltd. (Japan). Surfacestress measurements rely upon the accurate measurement of the stressoptical coefficient (SOC), which is related to the birefringence of theglass. SOC in turn is measured according to Procedure C (Glass DiscMethod) described in ASTM standard C770-16, entitled “Standard TestMethod for Measurement of Glass Stress-Optical Coefficient,” thecontents of which are incorporated herein by reference in theirentirety.

As used herein, DOC means the depth at which the stress in thechemically strengthened alkali aluminosilicate glass article describedherein changes from compressive to tensile. DOC may be measured by FSMor a scattered light polariscope (SCALP) depending on the ion exchangetreatment. Where the stress in the glass article is generated byexchanging potassium ions into the glass article, FSM is used to measureDOC. Where the stress is generated by exchanging sodium ions into theglass article, SCALP is used to measure DOC. Where the stress in theglass article is generated by exchanging both potassium and sodium ionsinto the glass, the DOC is measured by SCALP, since it is believed theexchange depth of sodium indicates the DOC and the exchange depth ofpotassium ions indicates a change in the magnitude of the compressivestress (but not the change in stress from compressive to tensile); theexchange depth of potassium ions in such glass articles is measured byFSM.

Refracted near-field (RNF) method or SCALP may be used to measure thestress profile. When the RNF method is utilized to measure the stressprofile, the maximum CT value provided by SCALP is utilized in the RNFmethod. In particular, the stress profile measured by RNF is forcebalanced and calibrated to the maximum CT value provided by a SCALPmeasurement. The RNF method is described in U.S. Pat. No. 8,854,623,entitled “Systems and methods for measuring a profile characteristic ofa glass sample”, which is incorporated herein by reference in itsentirety. In particular, the RNF method includes placing the glassarticle adjacent to a reference block, generating apolarization-switched light beam that is switched between orthogonalpolarizations at a rate of between 1 Hz and 50 Hz, measuring an amountof power in the polarization-switched light beam and generating apolarization-switched reference signal, wherein the measured amounts ofpower in each of the orthogonal polarizations are within 50% of eachother. The method further includes transmitting thepolarization-switched light beam through the glass sample and referenceblock for different depths into the glass sample, then relaying thetransmitted polarization-switched light beam to a signal photodetectorusing a relay optical system, with the signal photodetector generating apolarization-switched detector signal. The method also includes dividingthe detector signal by the reference signal to form a normalizeddetector signal and determining the profile characteristic of the glasssample from the normalized detector signal.

The stress profiles may also be determined from the spectra of boundoptical modes for TM and TE polarization by using the inverseWentzel-Kramers-Brillouin (IWKB) method as taught in U.S. Pat. No.9,140,543, the contents of which are hereby incorporated by reference inits entirety.

Described herein are strengthened glass articles having a stress profile(σ) that varies as a function (σ(x)) of position (x) within the glassarticle. The position (x) may refer to the depth into the glass articlefrom a surface thereof. The stress profile has a slope (S) at any pointthat is a first derivative of the stress (σ) with position (x); i.e.,S=(dσ/dx). The slope of a segment or portion of the stress profile thatclosely approximates a straight line is defined as the average slope forregions that are well approximated as straight segments. The slope rate(SR) or stress curvature of the stress profile is the second derivativeof the stress (σ) with position (x); i.e., SR=(d²σ/dx²).

A schematic cross-sectional view of the strengthened glass article isshown in FIG. 1 . Glass article 100 has a thickness t, a first surface110, and a second surface 112. Glass article 100, in some embodiments,has a thickness t of up to about 2 mm, and all ranges and subrangestherebetween, for example, from about 0.1 mm to about 2 mm in someembodiments, or from about 0.1 to about 1 mm in other embodiments. Whilethe embodiment shown in FIG. 1 depicts glass article 100 as a flatplanar sheet or plate, the glass article may have other configurations,such as three dimensional shapes or non-planar configurations. Glassarticle 100 has a first compressive layer 120 extending from firstsurface 110 to a depth of compression (DOC) d₁ into the bulk of theglass article 100. In the embodiment shown in FIG. 1 , glass article 100also has a second compressive layer 122 extending from second surface112 to a second depth of compression d₂. First and second compressivelayers 120, 122 are each under a compressive stress CS. In someembodiments, first and second compressive layers 120, 122 each have amaximum compressive stress at the first and second surfaces 110, 112,respectively. Glass article 100 also has a central region 130 thatextends from d₁ to d₂. Central region 130 is under a tensile stress orphysical center tension (CT), which balances or counteracts thecompressive stresses of compressive layers 120 and 122. The depths ofcompression d₁, d₂ of first and second compressive layers 120, 122protect the glass article 100 from the propagation of flaws introducedby sharp impact to first and second surfaces 110, 112 by minimizing thelikelihood of a flaw penetrating through the depth d₁, d₂ of first andsecond compressive layers 120, 122.

In one aspect, the stress in the strengthened glass article varies as afunction of the depth, and has a compressive layer extending from afirst surface of the glass to a depth of compression (DOC) or depth oflayer (DOL). The compressive layer is under a compressive stress (CS).The stress profile of the glass article is schematically shown in FIG.12 . A single ion exchange step forms a compressive layer extending fromthe surface of the glass to a first depth of compression (DOC1), wherethe compressive layer is under a first compressive stress (CS1). Thestress profile 305 obtained by the single ion exchange step may beeither linear or may be approximated by a complementary error function(erfc).

The cations from the ion exchange bath may then be diffused from thesurface of the glass to the center of the glass at a depth of t/2 in athermal diffusion step. In some embodiments, this is achieved byallowing the ion exchange to proceed for longer time periods (e.g., 16hours or more at 460° C.), and/or, in some embodiments, by a subsequentthermal diffusion (heating) step. The cations are allowed to diffusefrom opposite surfaces of the glass until the diffused cations meet atthe center of the glass 330. The thermal diffusion step in someembodiments results in a decrease in the compressive stress at thesurface to a second compressive stress (CS2) and an increase in thedepth of compression to a second depth of compression (DOC2) such thatCS2≤CS1 and DOC2>DOC1.

The thermal diffusion step, in some embodiments, includes heating theglass to a temperature in a range from about 400° C. to about 500° C.for times ranging from at least about 0.5 hour to about 40 hours.

The slope (S1) following the first ion exchange step, expressed asCS1/DOC where CS1 is the compressive stress at the surface of the glassafter the first ion exchange step, the absolute value of slope S1 (|S1|)is in a range from about 0.5 MPa/um to about 30 MPa/μm. In someembodiments, the slope (S1) has an absolute value (|S1|), where 1.2MPa/μm≤|S1|≤20 MPa/μm, 1.5 MPa/μm≤|S1|≤15 MPa/μm, and all ranges andsubranges therebetween. In still other embodiments, slope (S1) has anabsolute value |S1| in a range from about 0.6 MPa/μm to about 15 MPa/um,0.8 MPa/μm≤|S1|≤10 MPa/μm, 1.5 MPa/μm≤|S1|≤10 MPa/μm, and all ranges andsubranges therebetween.

Following the thermal diffusion step, the glass has a stress profile300, schematically shown in FIG. 12 , comprising a first region 310extending from the first surface to a depth (d1) into the glass, whereind1>0.06t and wherein at least a portion of the first region has a firstslope (m1), and a second region 320 extending from a depth of at leastd1 to the second depth of compression (DOC2) and having a second slope(m2), wherein |m1|≤|m2|. In some embodiments, as shown for example inFIG. 13 , the slope of the stress profile at d1 may be zero, meaning thefirst derivative of the stress profile at d1 ((dσ/dx), where x=d1) iszero. In some embodiments, the stress profile contains a negativecurvature and d1 may be at the point of the maximum absolute value ofthe negative curvature. In some embodiments, the first slope (m1) isgreater than or equal to zero (m1>0) and the second slope (m2) isnegative (m2<0).

In some embodiments, the glass article is strengthened by a two-step ionexchange process. Here the glass article is ion exchanged a second timefollowing the thermal diffusion step. The second ion exchange is carriedout in an ion exchange bath that differs in composition from the firstion exchange bath. The stress profile 350 obtained following the secondion exchange step is schematically shown in FIG. 13 . The second step ofthe ion exchange process provides a compressive stress “spike” 312—i.e.,a sharp increase in compressive stress—in a sub-region of first region310, where the sub-region is adjacent to the surface of the glassarticle, extends to a second depth (d2) below the surface, and has amaximum compressive stress (CS). In some embodiments, d2<d1. Followingthe second ion exchange step, the slope of the spike region 312 (m3) hasan absolute value (|m3|) in a range from about 30 MPa/μm to about 200MPa/μm (30 MPa/μm≤|m3|≤200 MPa/μm). In some embodiments, 40MPa/μm≤|m3|≤160 MPa/μm, other embodiments 50 MPa/μm≤|m3|≤200 MPa/μm,and, in still other embodiments, 45 MPa/μm≤|m3|≤120 MPa/μm. In someembodiments, |m1|<|m3|.

Stress profiles observed for samples that were subjected to a first ionexchange followed by thermal treatment and second ion exchange asdescribed herein are plotted in FIG. 14 . Conditions that were used totreat the samples are also included in the figure. All samples exhibit asharp increase in compressive stress or “spike” near the surface and aregion having some degree of negative curvature.

In those embodiments in which the glass article is strengthened by asingle-step ion exchange process, the slope S, which is expressed asCS/DOC, has an absolute value in a range from about 0.5 MPa/μm (or 88MPa/(88 μm/2)) to about 200 MPa/μm (or 1,000 MPa/5 μm). In otherembodiments, the slope (S), has an absolute value (|S|) in a range fromabout 0.6 MPa/μm (or 88 MPa/140 μm) to about 200 MPa/μm (or 1,000 MPa/5μm).

The slope rate (SR) of the stress profile in the compressive layerbetween the surface and the depth of compression (DOC) includes at leastone region where the SR value changes sign, indicating that the slope(S) of the stress profile is not a monotonically increasing ordecreasing function. Instead, the slope (S) changes from a decreasing toan increasing pattern or vice-versa, thus defining a S-shaped region ofthe stress profile.

In some embodiments, the depth of compression is at least 20% of thethickness; i.e., DOC≥0.2t. The depth of compression (DOC), in someembodiments, is in a range from about 0.05t to about 0.35t, and allranges and subranges therebetween, for example, in some embodiments fromabout 0.14t to about 0.35t, in other embodiments from about 0.15t toabout 0.25t, and in still other embodiments, from about 0.20t to about0.25t. The thickness (t) of the strengthened glass article is in a rangefrom about 0.1 mm to about 2 mm, such as about 0.4 mm or less.

The compressive layer, in some embodiments, may further comprise anear-surface region having a compressive stress (CS) at the surface in arange from about 50 MPa to about 1,000 MPa or, in other embodiments,from about 500 MPa to about 2,000 MPa, and all ranges and subrangestherebetween. The stress profile in the compressive stress layer mayfurther include a first sub-region having a negative curvature and asecond sub-region having a positive curvature. As used herein, the term“negative curvature” means that the stress profile in that region isconcaved downward and “positive curvature” means that the stress profilein that region is concaved upward. In some embodiments, the absolutevalue of the negative curvature exceeds 10 MPa/(t(mm))² over asub-region whose spatial extent ranges from about 2% to about 25% of thethickness (t). In some embodiments, the maximum absolute value of thenegative curvature is between about 20 MPa/(t(mm))² and about 4,000MPa/(t(mm))², and all ranges and subranges therebetween, for example, insome embodiments, from about 40 MPa/(t(mm))² to about 2000 MPa/(t(mm))²,and, in still other embodiments, from about 80 MPa/(t(mm))² to about1,000 MPa/(t(mm))². The stress profile in the second sub-region may, insome embodiments, include an inflection point. The physical centertension (CT) is in a range from about 40 MPa/(t(mm))^(1/2) to about 150MPa/(t(mm))^(1/2) and all ranges and subranges therebetween, forexample, in some embodiments, from about 42 MPa/(t(mm))^(1/2) to about100 MPa/(t(mm))^(1/2).

The curvature of the stress profile is measured by identifying a portionof a stress profile that is of interest. A quadratic polynomial fit isapplied to the portion of interest, with the resulting coefficient ofthe highest order term being the curvature of the portion of interest.The curvature will have units of MPa/mm² when the y-axis of the stressprofile is measured in MPa and the x-axis of the stress profile ismeasured in mm. Additionally, when the x-axis of the stress profile ismeasured in μm, the curvature may be converted to units of MPa/mm² bythe appropriate conversion factor.

In some cases the measured stress profile may include artifacts, ornoise, as a result of the measurement process. In such cases, theartifacts are removed before determining the curvature of the stressprofile to increase the accuracy of the calculated curvature. Theartifacts may be removed by any appropriate processing method known inthe art. For example, the artifacts may be removed by applying alow-pass filter to the stress profile or to the TE and TM index profiles(for example, when the IWKB method is used to determine the stressprofile) from which the stress profile is extracted.

In some embodiments, the compressive stress within the compressive layermay decrease from a maximum compressive stress (CS) at the surface ofthe glass article to less than 50% of the maximum compressive stresswithin a depth of less than about 8 μm below the surface.

In some embodiments, the glass article is ion exchanged and annealed(i.e., subjected to a thermal diffusion step). In particularembodiments, the glass is ion exchanged in a single-step ion exchange(SIOX) process followed by an annealing process. In other embodiments,the ion exchange process is a two-step or dual ion exchange (DIOX)process comprising a first ion exchange step followed by an optionalthermal anneal or diffusion step, which is then followed by a second ionexchange step in which the first ion exchange bath has a compositionthat is different from that of the second ion exchange bath. In someembodiments, the second ion exchange bath comprises at least 90% KNO₃ byweight and less than 10% NaNO₃ by weight. In other embodiments, thesecond ion exchange bath comprises at least 95 wt % KNO₃ with NaNO₃accounting for the balance of the bath. In still other embodiments, thesecond ion exchange bath contains essentially 100% KNO₃ by weight. Thesecond ion exchange step adds a compressive stress “spike”—i.e., a sharpincrease in compressive stress—in the region immediately adjacent to thesurface of the glass.

In those embodiments in which a single-step ion exchange process is usedto strengthen the glass article, the article is ion exchanged at atemperature ranging from about 300° C. to about 500° C. in an ionexchange bath containing from about 25% to about 100% KNO₃ and 0% toabout 75% NaNO₃ by weight. The ion exchange bath may include othermaterials, such as silicic acid or the like, to improve bathperformance.

The glasses described herein are ion exchangeable alkali aluminosilicateglasses, which, in some embodiments, are formable by down-drawprocesses, such as slot-draw, or fusion-draw processes that are known inthe art. In particular embodiments, such glasses may have a liquidusviscosity of at least about 100 kiloPoise (kP), or at least about 130kP. In one embodiment, the alkali aluminosilicate glass comprises SiO₂,Al₂O₃, P₂O₅, and at least one alkali metal oxide (R₂O), wherein0.75≤[(P₂O₅(mol %)+R₂O(mol %))/M₂O₃ (mol %)]≤1.2, where M₂O₃=Al₂O₃+B₂O₃.In some embodiments, the alkali aluminosilicate glass comprises orconsists essentially of: from about 40 mol % to about 70 mol % SiO₂;from 0 mol % to about 28 mol % B₂O₃; from 0 mol % to about 28 mol %Al₂O₃; from about 1 mol % to about 14 mol % P₂O₅; and from about 12 mol% to about 16 mol % R₂O and, in certain embodiments, from about 40 toabout 64 mol % SiO₂; from 0 mol % to about 8 mol % B₂O₃; from about 16mol % to about 28 mol % Al₂O₃; from about 2 mol % to about 12 mol %P₂O₅; and from about 10 to about 16 mol % R₂O, or from about 12 mol % toabout 16 mol % R₂O, where R₂O includes Na₂O. In some embodiments, 11 mol%≤M₂O₃≤30 mol %; in some embodiments, 13 mol %≤R_(x)O≤30 mol %, whereR_(x)O is the sum of alkali metal oxides, alkaline earth metal oxides,and transition metal monoxides present in the glass. In someembodiments, the glass is lithium-free. In other embodiments, the glassmay comprise up to about 10 mol % Li₂O, or up to about 7 mol % Li₂O.These glasses are described in U.S. patent application Ser. No.13/305,271, granted as U.S. Pat. No. 9,346,703, entitled “IonExchangeable Glass with Deep Compressive Layer and High DamageThreshold,” filed Nov. 28, 2011, by Dana Craig Bookbinder et al. andclaiming priority from U.S. Provisional Patent Application No.61/417,941, filed on Nov. 30, 2010, and having the same title, thecontents of which are incorporated herein by reference in theirentirety.

In certain embodiments, the alkali aluminosilicate glass comprises atleast about 2 mol % P₂O₅, or at least about 4 mol % P₂O₅, wherein(M₂O₃(mol %)/R_(x)O(mol %))<1, wherein M₂O₃=Al₂O₃+B₂O₃, and whereinR_(x)O is the sum of monovalent and divalent cation oxides present inthe alkali aluminosilicate glass. In some embodiments, the monovalentand divalent cation oxides are selected from the group consisting ofLi₂O, Na₂O, K₂O, Rb₂O, Cs₂O, MgO, CaO, SrO, BaO, and ZnO. In someembodiments, the glass is lithium-free and comprises or consistsessentially of from about 40 mol % to about 70 mol % SiO₂; from about 11mol % to about 25 mol % Al₂O₃; from about 2 mol % P₂O₅, or from about 4mol % to about 15 mol % P₂O₅; from about 10 mol % Na₂O, or from about 13mol % to about 25 mol % Na₂O; from about 13 to about 30 mol % R_(x)O,where R_(x)O is the sum of the alkali metal oxides, alkaline earth metaloxides, and transition metal monoxides present in the glass; from about11 mol % to about 30 mol % M₂O₃, where M₂O₃=Al₂O₃+B₂O₃; from 0 mol % toabout 1 mol % K₂O; from 0 mol % to about 4 mol % B₂O₃, and 3 mol % orless of one or more of TiO₂, MnO, Nb₂O₅, MoO₃, Ta₂O₅, WO₃, ZrO₂, Y₂O₃,La₂O₃, HfO₂, CdO, SnO₂, Fe₂O₃, CeO₂, As₂O₃, Sb₂O₃, Cl, and Br; wherein1.3<[(P₂O₅+R₂O)/M₂O₃]≤2.3, where R₂O is the sum of monovalent cationoxides present in the glass. In some embodiments, the glass islithium-free. In other embodiments, the glass may comprise up to about10 mol % Li₂O, or up to about 7 mol % Li₂O. The glass is described inU.S. Pat. No. 9,156,724 by Timothy M. Gross, entitled “Ion ExchangeableGlass with High Crack Initiation Threshold,” filed Nov. 15, 2012, andU.S. Pat. No. 8,756,262 by Timothy M. Gross, entitled “Ion ExchangeableGlass with High Crack Initiation Threshold,” filed Nov. 15, 2012, bothclaiming priority to U.S. Provisional Patent Application No. 61/560,434filed Nov. 16, 2011. The contents of the above patent and applicationsare incorporated herein by reference in their entirety.

In other embodiments, the alkali aluminosilicate glass comprises SiO₂,Al₂O₃, P₂O₅, and greater than about 1 mol % K₂O, wherein the glass has acoefficient of thermal expansion (CTE) of at least about 90×10⁻⁷° C.⁻¹.In some embodiments, the glass comprises or consists essentially of:from about 57 mol % to about 75 mol % SiO₂ (i.e., 57 mol % SiO₂≤75 mol%); from about 6 mol % to about 17 mol % Al₂O₃(i.e., 6 mol % Al₂O₃17 mol%); from about 2 mol % to about 7 mol % P₂O₅ (i.e., 2 mol % P₂O₅≤7 mol%); from about 14 mol % to about 17 mol % Na₂O (i.e., 14 mol % Na₂O≤17mol %); and greater than about 1 mol % to about 5 mol % K₂O (i.e., 1 mol%<K₂O≤5 mol %). In some embodiments, the glass comprises or consistsessentially of or comprises: from about 57 mol % to about 59 mol % SiO₂(i.e., 57 mol %≤SiO₂≤59 mol %); from about 14 mol % to about 17 mol %Al₂O₃(i.e., 14 mol %≤Al₂O₃≤17 mol %); from about 6 mol % to about 7 mol% P₂O₅ (i.e., 6 mol %≤P₂O₅≤7 mol %); from about 16 mol % to about 17 mol% Na₂O (i.e., 16 mol %≤Na₂O≤17 mol %); and greater than about 1 mol % toabout 5 mol % K₂O (i.e., 1 mol %<K₂O≤5 mol %). In certain embodiments,the glass further comprises up to about 2 mol % MgO (i.e., 0 mol %≤MgO≤2mol %) and/or up to about 1 mol % CaO (i.e., 0 mol %≤CaO≤1 mol %). Insome embodiments, the glass is substantially free of MgO. In someembodiments, the glass is substantially free of B₂O₃ and/or lithium orLi₂O. These glasses are described in U.S. patent application Ser. No.14/465,888, published as U.S. Patent Application Publication No.2015/0064472, entitled “Damage Resistant Glass with High Coefficient ofThermal Expansion,” filed Aug. 22, 2014, by Timothy M. Gross et al. andclaiming priority from U.S. Provisional Patent Application No.61/870,301, filed on Aug. 27, 2013, and having the same title, thecontents of which are incorporated herein by reference in theirentirety.

In another aspect, a method of strengthening a glass having a thickness(t) and achieving the stress profiles described herein is provided. Themethod comprises immersing the glass in an ion exchange bath comprisingalkali cations (e.g., K⁺) that are different from alkali cations (e.g.,Na⁺, Li⁺) that are present in the glass, and replacing alkali cationswithin the glass with the alkali cations from the ion exchange bath. Theion exchange forms a compressive layer extending from the surface of theglass to a first depth of compression (DOC1), where the compressivelayer is under a first compressive stress (CS1).

The cations from the ion exchange bath are then diffused from thesurface of the glass to the center of the glass at a depth of t/2. Insome embodiments, this is achieved by allowing the ion exchange tocontinue for longer periods (e.g., 16 hours or more at 460° C.), and/or,in some embodiments, by a subsequent thermal diffusion (heating) step.The cations are allowed to diffuse from opposite surfaces of the glassuntil the diffused cations meet at the center of the glass. Thediffusion step in some embodiments results in a decrease in thecompressive stress at the surface to a second compressive stress (CS2)and an increase in the depth of compression to a second depth ofcompression (DOC2) such that CS2≤CS1 and DOC2>DOC1.

The thermal diffusion step, in some embodiments, includes heating theglass to a temperature in a range from about 400° C. to about 500° C.for times ranging from 0.5 hour to 40 hours.

In some embodiments, the method may further include a second ionexchange following either the first ion exchange or the thermaldiffusion step. As previously described hereinabove, the second ionexchange bath has a composition that is different from that of the firstion exchange bath. In some embodiments, the second ion exchange bathcomprises at least 90% KNO₃ by weight and less than 10% NaNO₃ by weight.In other embodiments, the second ion exchange bath comprises at least 95wt % KNO₃ with NaNO₃ accounting for the balance of the bath. In stillother embodiments, the second ion exchange bath contains essentially100% KNO₃ by weight. The second ion exchange step adds a compressivestress “spike”—i.e., a sharp increase in compressive stress—in theregion immediately adjacent to the surface of the glass, creating athird compressive stress (CS3) at the surface, where CS3>CS1.

Under ideal conditions, the shape and values of the stress profile in anion exchanged glass should obey a classic diffusion equation. Thesolution for this equation indicates that, in the case of a singleboundary through which the ions diffuse without limit, the stressprofile should be a complementary error function (erfc(x)). As usedherein, the terms “error function” and “erf” refer to the function thatis twice the integral of a normalized Gaussian function between 0 and

$\frac{x}{\sigma \sqrt{}2 }.$

The terms “complementary error function” and “erfc” are equal to oneminus the error function; i.e., erfc(x)=1−erf(x). For a boundedcase—e.g., where ions diffuse from opposite surfaces to the center ofthe glass—diffusion of strengthening cations follows a complementaryerror function until the ions meet at the center of the glass, afterwhich the whole diffusion profile may be better approximated by aparabolic shape profile for the ionic distribution. The stress profileis directly related to the ionic distribution inside the glass. Thestress profile should therefore be similar to the ionic distribution,regardless of whether the distribution of ions according to acomplementary error function or a parabolic function.

A significant divergence between expected and observed stress profilesmay occur for certain glasses. This is likely due to stress relaxationpresent in the glass and additional annealing effects. Modeled andmeasured stress profiles of ion exchanged glass having a nominalcomposition of about 57 mol % SiO₂, 0 mol % B₂O₃, about 17 mol % Al₂O₃,about 7% P₂O₅, about 17 mol % Na₂O, about 0.02 mol % K₂O, and about 3mol % MgO and a thickness of 800 μm are plotted over a wide range ofdiffusion times in FIG. 2 . The glass was ion exchanged at 460° C. in amolten salt bath of 20 wt % NaNO₃/80 wt % KNO₃ for times ranging from 16hours to about 184 hours. The modeled stress profiles were fordiffusion/ion exchange times of 16 hours, 40 hours, 64 hours, 135 hours,159.25 hours, and 183.53 hours. The stress profiles were also measuredby SCALP (polarimetry) for a diffusion/ion exchange time of 183.43 hoursand by IWKB for diffusion/ion exchange times of 16 hours, 40 hours, 64hours, and 159.25 hours. For diffusion times of 16 hours and 40 hours,the modeled stress profiles (dashed lines a and b, respectively, in FIG.2 ) are still based on a complementary error function. For longerdiffusion times (64, 135, 159.25, and 183.53 hours), the diffused ionshave met at the center of the glass sample, leading in theory to aparabolic-like profile. In practice however, stress relaxation in theglass and/or additional thermal annealing cause the real measuredstresses to diverge from the theoretical predicted values. In this case,an S-shape stress profile is generated. The degree of divergence betweenthe theoretical and experimental stress profiles will depend on theparticular characteristics of the glass and processing conditions. Someglasses will be more susceptible than other glasses to variations underthe same process conditions. As seen in FIG. 3 , significant differencesstart to occur for this particular glass composition for ion exchange at460° C. for times of 16 hours or greater.

A more detailed view of the stress profile in FIG. 2 is shown in FIG. 3. The rounding effect observed for the compressive stress (CS) profileat the surface may be on the order of a few percent of the target CSafter 16 hours of diffusion/ion exchange at 460° C. (a in FIG. 3 ) togreater than 100% of the target after 183.53 hours of diffusion/ionexchange at 460° C. (b in FIG. 3 ). The progression of the roundingeffect is clearly observed as the diffusion time increases. Also, theslope of the stress profile changes depending on the time andtemperature of ion exchange: the second derivative of the stress profilechanges, creating an inflection point in the stress profile and adecrease in the absolute value of slope. The inflection point willhappen somewhere in the compressive region of the stress profile betweenthe surface of the glass and the depth of compression (DOC), regardlesswhether the stress profile is a complementary error function (erfc(x))or is parabolic.

Further details of modeled (dashed line) and experimentally determined(solid line) stress profiles for the case of 40 hour diffusion/ionexchange at 460° C. are shown in FIG. 4 . Here, the modeled stressprofile is still a complementary error function erfc(x), having a deepdepth of compression (DOC), which is the position at which the stress iszero inside the sample. The profiles shown in FIG. 4 demonstrate thaterror-function stress profiles do not include S-shaped profiles of thetype described herein.

The S-shaped stress profile may occur in instances when glass is ionexchanged in a bath that is “poisoned” to a particular level (e.g.,comprising greater than 30 wt % NaNO₃). Modeled (dashed lines) andmeasured (solid lines) stress profiles for 800 μm thick glass having anominal composition of about 57 mol % SiO₂, 0 mol % B₂O₃, about 17 mol %Al₂O₃, about 7% P₂O₅, about 17 mol % Na₂O, about 0.02 mol % K₂O, andabout 3 mol % MgO are shown in FIG. 5 . The glass was ion exchanged(IOX) in a bath of pure (100% by weight) KNO₃ for different temperaturesand times (IOX at 460° C. for 60 hours and IOX at 490° C. for 32 hours).

The modeled stress profiles directly overlap each other, and thus showthat the expected diffusion profile based on a diffusion length of2(D×Time)^(1/2), where D is the diffusion coefficient at a certaintemperature, is basically the same for the different cases investigated.Therefore, one would expect that the diffusion at 460° C. for 60 hours(line a in FIG. 5 ) and the diffusion at 490° C. for 32 hours (line b inFIG. 5 ) would produce the same stress profile. A modeled complementaryerror function erfc(x) stress profile is shown as a dashed line in FIG.5 for comparison purposes. In practice, however, the combination of timeand temperature leads to a different level of relaxation in the glassand results in different stress profiles. This can be observed by themeasurements performed using the IWKB treatment for these samples, whichshows that the samples have different stress profiles, surfacecompressive stresses (CS), and depths of compression (DOC). The DOCvalues determined for both samples shown in FIG. 5 are greater than thetheoretical value of about 21% of the thickness (0.21t). In the case ofglass ion exchanged at 490° C. for 32 hours, the depth of compression(DOC) is 25% of the thickness (0.25t). Despite being frangible, bothsamples shown in FIG. 5 demonstrated excellent performance when droppedonto 30 grit sandpaper, surviving average drop heights of 148 cm (IOX at490° C.) and 152 cm (IOX at 460° C.). Since the ions diffusing fromopposite surfaces of the glass met at the center of these samples, thesamples were expected to have a parabolic stress profile, but theresulting stress profiles are S-shaped. Although diffusion theory wouldpredict that the absolute value of the slope would increase or stayapproximately constant, the absolute values of the slope of the observedstress profiles begin to decrease at a depth of about 120 μm. Thisinflection or reduction in slope towards the surface is one of the maincharacteristics of these S-shaped stress profiles.

Energy (surface, stored, total), physical center tension (CT), surfacecompressive stress (CS), depth of compression (DOC), and results ofmechanical testing (4-point bend testing, abraded ring-on-ring (AROR),and drop onto 30 grit sandpaper) for the samples shown in FIG. 5 arelisted in Table 1.

TABLE 1 Stress profile parameters and mechanical performance measuredfor samples shown in FIG. 5. IOX at 490° C. IOX at 460° C. 32 hours 60hours Energy surface (J/m²) 929.28 1329.45 Energy stored (J/m²) 929.28653.99 Energy total (J/m²) 1858.57 1983.44 CT (MPa) 217 233 CS (MPa) 294402 DOC (μm) 191 179 4-point bend (MPa) 247 AROR 45 psi (kgf) 58 Droponto 30 grit 148 152 sandpaper (cm avg)

The strengthened glass articles described herein also demonstrateimproved surface strength when subjected to abraded ring-on-ring (AROR)testing. The strength of a material is defined as the stress at whichfracture occurs. The abraded ring-on-ring test is a surface strengthmeasurement for testing flat glass specimens, and ASTM C1499-09(2013),entitled “Standard Test Method for Monotonic Equibiaxial FlexuralStrength of Advanced Ceramics at Ambient Temperature,” serves as thebasis for the ring-on-ring abraded ROR test methodology describedherein. The contents of ASTM C1499-09 are incorporated herein byreference in their entirety. The glass specimen was abraded prior toring-on-ring testing with 90 grit silicon carbide (SiC) particles thatare delivered to the glass sample using the method and apparatusdescribed in Annex A2, entitled “abrasion Procedures,” of ASTMC158-02(2012), entitled “Standard Test Methods for Strength of Glass byFlexure (Determination of Modulus of Rupture). The contents of ASTMC158-02 and the contents of Annex 2 in particular are incorporatedherein by reference in their entirety.

Prior to ring-on-ring testing a surface of the glass sample was abradedas described in ASTM C158-02, Annex 2, to normalize and/or control thesurface defect condition of the sample using the apparatus shown in FIG.A2.1 of ASTM C158-02. The abrasive material is sandblasted onto thesample surface at a load of 15 psi using an air pressure of 45 psi.After air flow was established, 5 cm³ of abrasive material was dumpedinto a funnel and the sample was sandblasted for 5 seconds afterintroduction of the abrasive material.

Stress profiles measured for a different ion exchangeable alkalialuminosilicate glass, which is described in U.S. patent applicationSer. No. 14/465,888, published as U.S. Patent Application PublicationNo. 2015/0064472, which was ion exchanged at 460° C. for 28 hours, areshown in FIG. 6 . Ion exchange was conducted in a mixed KNO₃/NaNO₃ bath.The amount of NaNO₃ in the bath was increased from 25 wt % (line a inFIG. 6 ) to 30 wt % (line below line a in FIG. 6 ) to 35 wt % (lineabove line b in FIG. 6 ), and finally, to 41 wt % (line b in FIG. 6 ),while the amount of KNO₃ was decreased between 75 wt % to 70 wt %, to 65wt %, and, finally, to 59 wt %. The stress profile obtained for glassion exchanged at 460° C. for 28 hours in a bath containing 41 wt % NaNO₃(solid line) and the modeled stress profile (dashed line) are shown inFIG. 7 . Because the ions diffusing from opposite surfaces of the glasshad met at the center of the sample, these samples were expected to haveparabolic stress profiles. However, the experimentally measured stressprofiles shown in FIGS. 6 and 7 are S-shaped. Although diffusion theorywould predict that the absolute value of the slope would increase orstay approximately constant, the absolute values of the slope of theobserved stress profiles begin to decrease at a depth of about 120 μm.This inflection or reduction in slope towards the surface is one of themain characteristics of these S-shaped stress profiles.

Other examples of S-shape stress profiles are shown in FIGS. 8, 9, and10 . In FIG. 8 , modeled (dashed line) and measured stress profiles(solid lines) of a glass having a thickness of 500 μm and a nominalcomposition of about 57 mol % SiO₂, 0 mol % B₂O₃, about 17 mol % Al₂O₃,about 7% P₂O₅, about 17 mol % Na₂O, about 0.02 mol % K₂O, and about 3mol % MgO. The glass was ion exchanged for 7 hours at 410° C. in a bathof 100 wt % KNO₃, and then thermally diffused by heating for 5 hours at450° C. to achieve a depth of compression (DOC)/depth of compressivelayer (DOCL) of 20% of the glass thickness (0.2t). These samples wereexpected to have a stress profile evolving from an error-functionprofile with some level of thermal relaxation at the surface to developa parabolic profile. In this particular example, the combination ofthermal annealing and additional stress relaxation in the glass resultedin a very pronounced difference from what was expected from diffusiontheory, and enabled deeper depths of compression to be achieved. FIGS. 9and 10 , illustrate how the process of ion exchange followed by thermaldiffusion can be used to create S-shape stress profiles having depths ofcompression of greater than 21% of the glass thickness. The examplesshown in FIGS. 9 and 10 have the same composition as those shown in FIG.8 . Sample thicknesses of 0.5 mm (500 μm) and 0.8 mm (800 μm) werestudied. However, the increase of depth of compression (DOC) to valuesgreater than 21% of the glass thickness may be extended well beyondthese illustrative examples to glasses having thicknesses ranging from0.1 mm (100 μm) to 2 mm.

Modeled stress profiles for glass having thicknesses of 0.8 mm and 0.5mm produced by a combination of ion exchange and thermal diffusion areshown in FIGS. 9 and 10 , respectively. The glass was ion exchanged for24 hours at 460° C. in a bath of pure (100 wt %) KNO₃ and thermaldiffusion by heating at 450° C. for times ranging from 5 hours to 24hours. As previously demonstrated, additional stress relaxation isexpected to take place, thus enabling the depth of compression (DOC) toextend to deeper depths within the glass and further accentuating theS-shape of the stress profile and reducing compressive stress at theglass surface. Based on the modeling shown in FIGS. 8-10 , it ispossible to predict that, after 10 hours of thermal annealing, thecompressive stress will be reduced and the depth of compressionDOC/depth of compressive layer DOCL will be further increased to wellabove 25% of the glass thickness.

Strengthened glasses having S-shaped stress profiles appear to have ahigher frangibility limit (i.e., the physical center tension (CT) abovewhich explosive fragmentation and ejection of small fragment occurs uponinsult or impact) than glasses having other profiles having a comparabledepth of compression (DOC). An example of an S-shaped profile obtainedfor 0.4 mm thick non-frangible glass having a nominal composition ofabout 57 mol % SiO₂, 0 mol % B₂O₃, about 17 mol % Al₂O₃, about 7% P₂O₅,about 17 mol % Na₂O, about 0.02 mol % K₂O, and about 3 mol % MgO isshown in FIG. 11 . The glass was ion exchanged for 11.5 hours at 430° C.in a bath containing 17 wt % NaNO₃ and 83 wt % KNO₃, and then subjectedto a thermal treatment at 430° C. for 13.07 hours. The ion exchanged andheat treated sample was non-frangible even though the center tension(CT) of the glass was 117 MPa, which is higher than any previously valuemeasured for a non-frangible glass of 0.4 mm thickness. Accordingly, inone embodiment, the stress profile of the strengthened glass article hasa region of negative curvature of the compressive stress in thecompression region, with a peak curvature and a physical center tension(CT) that is generally higher than that typically observed forchemically strengthened glass. The absolute value of the peak curvatureis in a range from 20 MPa/t² to 4000 MPa/t², where t is the thickness ofthe glass, expressed in millimeters. The region where the absolute valueof the negative curvature exceeds 10 MPa/t² is in a range from about 2%of the thickness to about 25% of the thickness t of the glass article,and, in some embodiments, is in a range from about 2.5% to about 20% ofthe thickness t.

A glass article with a thickness of 0.4 mm was subjected to a first ionexchange, a thermal treatment, and a second ion exchange to form aS-shaped stress profile in the glass article. The glass article includeda glass containing about 57 wt % SiO₂, about 16 wt % Al₂O₃, about 17 wt% Na₂O, about 3 wt % MgO, and about 7 wt % P₂O₅. The first ion exchangewas carried out by immersing the glass article for 11 hours in a bathcontaining 38 wt % NaNO₃ and 62 wt % KNO₃ at a temperature of 450° C.The ion exchanged glass article was then subjected to thermal treatmentfor 6.5 hours at 420° C. The subsequent ion exchange was carried out byimmersing the thermally treated glass article for 11 minutes in a bathcontaining 0.5 wt % NaNO₃ and 99.5 wt % KNO₃ at a temperature of 390° C.

The index profiles for transverse magnetic (TM) and transverse electric(TE) guided light were extracted by the IWKB procedure and are shown inFIG. 15 . The raw stress profile extracted from the difference of theindex profiles is shown in FIG. 16 . The stress profile shown in FIG. 16demonstrates that a spike in compressive stress is present at thesurface of the glass article, a region of negative curvature from adepth of about 15 μm to an inflection point located between 80 μm and100 μm, and a region of positive curvature at larger depths. The rawstress profile include artifacts produced by differences in the turningpoints of corresponding optical modes in the TM and TE index profiles,with the artifacts being located at depths in the vicinity of andslightly deeper than the bottom of the compressive stress spike at thesurface (about 12 μm to about 40 μm). These artifacts can be smoothedbased on resemblance to the index profiles to obtain a more accuratestress profile. The compressive stress spike shown in FIG. 16 has amaximum of about 785 MPa and has a depth of about 10 μm, a region ofnegative curvature from a depth of about 15 μm to an inflection pointlocated at about the depth of compression (DOC), and a region ofpositive curvature at larger depths. The DOC of the stress profile inFIG. 16 is located about 84 μm (21% of the 0.4 mm thickness of the glassarticle). A region of constant tension may surround a mid-thicknessplane of the glass article, and the stress profile of FIG. 16 exhibits aphysical center tension (CT) of about 105 MPa.

The fabrication process that produces the stress profile shown in FIG.16 maintains the glass article in a non-frangible state throughout theprocess. This is an additional benefit that reduces the chance offracture of the glass article during the strengthening process. Thecompressive stress spike formed in the strengthened glass article guidesthree optical modes in each of the TM and TE polarization at awavelength of 595±5 nm. Compressive stress spikes with a depth ofgreater than about 9 μm and a maximum compressive stress of greater thanabout 700 MPa that are capable of confining at least three optical modesat 595 nm are capable of reducing fractures of the glass article due tooverstress of shallow flaws in the glass article surface duringfinishing operations performed on the glass article. Additionally, theregion of negative curvature that occurs between the bottom of the spike(about 15 μm) and a depth of the inflection point (comparable to thedepth of compression, about 90 μm) provides of a region of substantialcompressive stress in the depth range of about 0.4DOC to about 0.9DOC(about 34 μm to about 76 μm). This substantial compressive stress regionprovides improved resistance to fracture from deep damage introductions,such as those produced when the glass article is dropped on a roughsurface. In some embodiments, the depth of the inflection point may beabout 0.8DOC to about 1.2DOC.

The strengthened articles disclosed herein may be incorporated intoanother article such as an article with a display (or display articles)(e.g., consumer electronics, including mobile phones, tablets,computers, navigation systems, and the like), architectural articles,transportation articles (e.g., automotive, trains, aircraft, sea craft,etc.), appliance articles, or any article that requires sometransparency, scratch-resistance, abrasion resistance or a combinationthereof. An exemplary article incorporating any of the strengthenedarticles disclosed herein is shown in FIGS. 17 and 18 . Specifically,FIGS. 17 and 18 show a consumer electronic device 5100 including ahousing 5102 having front 5104, back 5106, and side surfaces 5108;electrical components (not shown) that are at least partially inside orentirely within the housing and including at least a controller, amemory, and a display 5110 at or adjacent to the front surface of thehousing; and a cover substrate 5112 at or over the front surface of thehousing such that it is over the display. In some embodiments, the coversubstrate 5112 may include any of the strengthened articles disclosedherein.

While typical embodiments have been set forth for the purpose ofillustration, the foregoing description should not be deemed to be alimitation on the scope of the disclosure or appended claims.Accordingly, various modifications, adaptations, and alternatives mayoccur to one skilled in the art without departing from the spirit andscope of the present disclosure or appended claims.

1. A glass article, comprising: opposing first and second surfacesdefining a thickness t; a center located at t/2; a stress profilecomprising: a compressive region extending from the first surface to adepth of compression (DOC); a maximum compressive stress (CS) within thecompressive region; a first region of the compressive region extendingfrom the first surface to a depth d1, wherein d1>0.06t, and at least aportion of the first region has a first slope m1; a second region of thecompressive region extending from d1 to the DOC, and having a secondslope m2, wherein |m1|≤|m2|; a first region sub-region extending fromthe first surface to a depth d2 and comprising a third slope m3, whereind2<d1, and |m1|<|m3|; and a compressive region sub-region within thecompressive region having a negative curvature.
 2. The glass article ofclaim 1, wherein the DOC is in a range from about 0.14t to about 0.35t.3. The glass article of claim 1, wherein the DOC is greater than orequal to 90 μm.
 4. The glass article of claim 1, wherein 30MPa/μm≤|m3|<200 MPa/μm.
 5. The glass article of claim 1, wherein the CSin a range from about 500 MPa to about 2,000 MPa.
 6. The glass articleof claim 1, wherein a spike compressive stress at d2 is greater than orequal to 150 MPa.
 7. The glass article of claim 1, wherein a maximumabsolute value of the negative curvature is at d1.
 8. The glass articleof claim 1, wherein a maximum absolute value of the negative curvatureis between 20 MPa/(t(mm))² and 4,000 MPa/(t(mm))².
 9. The glass articleof claim 1, wherein a slope of the stress profile at d1 is zero.
 10. Theglass article of claim 1, wherein d2 is less than or equal to 8 μm. 11.The glass article of claim 1 having a planar configuration, wherein t isin a range from about 0.1 mm to about 1 mm.
 12. The glass article ofclaim 1, wherein the negative curvature has an absolute value exceeding10 MPa/(t(mm))² over a spatial extent ranging from about 2% to about 25%of t.
 13. The glass article of claim 1, wherein the maximum compressivestress CS is at the first surface, and at a depth of less than about 8μm below the first surface a compressive stress of the article decreasesto less than 50% of the maximum compressive stress CS.
 14. The glassarticle of claim 1, further comprising a physical center tension in arange from about 40 MPa/(t(mm))^(1/2) to about 150 MPa/(t(mm))^(1/2).15. The glass article of claim 1, wherein the glass article comprises atleast about 4 mol % P₂O₅, wherein (M₂O₃(mol %)/R_(x)O(mol %))<1, whereM₂O₃=Al₂O₃+B₂O₃, and where R_(x)O is a sum of monovalent and divalentcation oxides present in the glass article.
 16. The glass article ofclaim 1, wherein the glass article comprises: about 40 mol % to about 70mol % SiO₂; about 11 mol % to about 25 mol % Al₂O₃; about 2 mol % toabout 15 mol % P₂O₅; about 10 mol % to about 25 mol % Na₂O; about 10 toabout 30 mol % R_(x)O, where R_(x)O is a sum of alkali metal oxides,alkaline earth metal oxides, and transition metal monoxides present inthe glass article.
 17. A glass article, comprising: opposing first andsecond surfaces defining a thickness t; a center located at t/2; astress profile comprising: a compressive region extending from the firstsurface to a depth of compression (DOC) that is greater than or equal to90 μm; a maximum compressive stress (CS) within the compressive regionin a range from about 500 MPa to about 2,000 MPa; a first region of thecompressive region extending from the first surface to a depth d1,wherein d1>0.06t, and at least a portion of the first region has a firstslope m1; a second region extending from d1 to the DOC, and having asecond slope m2, wherein |m1|≤|m2|; a first region sub-region extendingfrom the first surface to a depth d2 and comprising a third slope m3,wherein: d2<d1, and |m1|<|m3| and 30 MPa/μm≤|m3|≤200 MPa/μm; a spikecompressive stress at d2 that is greater than or equal to 150 MPa; and acompressive region sub-region within the compressive region with anegative curvature.
 18. The glass article of claim 17 having a planarconfiguration, wherein t is in a range from about 0.1 mm to about 1 mm.19. The glass article of claim 17, wherein the negative curvature has anabsolute value exceeding 10 mPa/(t(mm))² over a spatial extent rangingfrom about 2% to about 25% of t.
 20. A consumer electronic product,comprising: a housing having a front surface, a back surface, and sidesurfaces; electrical components provided at least partially within thehousing, the electrical components including at least a controller, amemory, and a display, the display being provided at or adjacent thefront surface of the housing; and the glass article of claim 17 disposedover the display.